|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's image uses a new formula, which is simply yesterday's formula with initial 'b' generalized rather than set to 0,0. This might give a little more variety to the images it draws. I named the new formula HyperMandelbrot2. Today's image is named "Pentagon Heptagon" because of the very prominent pentagon. And there is also a heptagon, much smaller and closer to the center. And yes, the series of polygons with an odd number of sides does continue indefinitely. An outzoom will reveal a triangle, while a couple inzooms will reveal a nonagon, a hendecagon, and a tridecagon. (I think these are the right names for polygons of 9, 11 and 13 sides.) How far the series goes beyond this point is anybody's guess, but I suspect that, like so much else in the world of fractals, it continues without limit. I have made no effort to figure out the number series of the arms stretching between the polygons, though it probably has a logical order. But at the same time, I see that the arms within the pentagon are unevenly distributed. Two of the pentagon vertexes have arms connecting with them from within, while the other three are cut off from the center. Today's coordinates define a blank area in the classic Mandelbrot set. If real(p3) and real(p4) are set to zero, the result is a flat black screen. The area actually lies somewhat inside the main bay of the M-set. Even though I have no idea how today's image ranks among Seahorse Valley images of the HyperMandelbrot set, I have rated it at an 8. Its mathematical interest is enough to be worth at least that rating. The calculation time of 4-1/4 minutes is fast enough to keep impatience at bay. And if it is not, the finished image will soon be available on the FOTD web site at: Friday was bright and sunny here at Fractal Central, but it was also cold and blustery, making it a rather unpleasant day to be outside. The high temperature of 27F -3C felt cold even in the strongest sun. With numerous sources of heat inside F.C., the fractal cats had their problem deciding where to spend the day. I had no such problem however. I spent the day working, then searching for a FOTD. As today's image shows, I was successful. And the next FOTD image will be posted in 24 hours. Until then, take care, and where's it at? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Pentagon-Heptagon { ; time=0:04:14.05-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot2 passes=t periodicity=0
center-mag=-0.749480813398176/+0.031703452082799/3\
.321327e+010/1/89/0 params=0/0/0/0/0.2/0/1e-020/0
float=y maxiter=3600 inside=0
colors=000mL6lM9lNBlODlPFlQIlRKlSMlTOlURlVTlWVlXXk\
`_lYZmWYnUXnSXoQWpOVpMVqKUrITtCTrGTqJToMTnPTlSTkVT\
iYTh`TfcTjcYecT`cPXcKScGNcBMc4Jc7HcAEcCCcF9cI7cK4d\
N2cQ0cSgcaXcZKcVNcXQcZSc`VcbYcc_cebdgefigikjklmnno\
pzrszuuzzzzvtzvrzupvunrtkmtihsgcse`sbYr`VrZTqXQqUN\
pSLpQIpOGrJPsFYuBev7nt9Bw3vu4ss5pq6mo7jm8gk9di9agA\
ZeBWcCTaDQ_ENa7GZEKWKOURSRXWzz_zzczzfzzbzzZzzVzzRz\
zOifKndGrcCva8z`5tb6oc7ie8df9ZhAUiBOkCJlDDnE8oEAnF\
CmFEmGGlGIlHKkHMkIOjIUiJZiJchKhhKmgLrgLvkMwkMwlRwq\
NwrJwwGwxCws8wt6vt5rp4mp3hq7cmAZmKUnUPmcKmmFlvAnz5\
oz3pz3qz4lz4gm4bc5ZZ5UZ6UY6dY7dY7dY5sa7nY9jVBfRDaO\
FYKDUFGUHJUILUKOULQUNTUOVUQYUR_UTbUUdUWgUXiUYkRalO\
dnLgoJjlMeiOagRYdTUaWP_YLX`HUbDPb8Sd9VeAXgB_hCbiDd\
kEglFjmBimFijIhgLhcOg`RgYVfUYfR`eOceKfdHjdEmcApc7s\
c4va5r`5o_6kY6hX6dW7aV7YT7VS8RR8OV4RQ8LLBGGFA8H2CI\
5GI8KIBNJERJHVJKZJNaKQeKT }
frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
|
times.
